## Sum to n terms of an Arithmetic progression - Advance

The sum of n terms of AP is the sum(addition) of first n terms of the arithmetic sequence. It is equal to n divided by 2 times the sum of twice the first term – 'a' and the product of the difference between second and first term-'d' also known as common difference, and (n-1), where n is numbers of terms to be added.

Q1.  If the ratio of the sum of n terms of two A.P.'s be (7n+1) : (4n+27), then the ratio of their 11th terms will be

•   2:3
•  3:4
•  4:3
•   5:6

4:3

Q2. The sum of integers from 1 to 100 that are divisible by 2 or 5 is

•  3000
•  3050
•  4050
•  None of these

3050

Q3.  If the sum of first n terms of an A.P. be equal to the sum of its first m terms, (m  n), then the sum of its first (m + n) terms will be

•   0
•  n
•  m
•  m + n

0

Q4.  The nth term of an A.P. is . Choose from the following the sum of its first five terms

•   14
•   35
•  80
•  40

40

Q5.  If the sum of two extreme numbers of an A.P. with four terms is 8 and product of remaining two middle term is 15, then greatest number of the series will be

•  5
•  7
•  9
•  11

7

Q6.  If the sum of the first 5n2+2n terms of a series be then its second term is

•  7
•   17
•  24
•  42

17

Q7. All the terms of an A.P. are natural numbers. The sum of its first nine terms lies between 200 and 220. If the second term is 12, then the common difference is

•   2
•  3
•  4
•  None of these

4

Q8.  In the arithmetic progression whose common difference is non-zero, the sum of first 3n terms is equal to the sum of the next n terms. Then the ratio of the sum of the first 2n terms to the next 2n terms is

•  1/5
•   2/3
•   3/4
•   None of these

1/5

Q9.  If the sum of n terms of an A.P. is nA + n2B where A, B are constants, then its common difference will be

•  A – B
•   A + B
•   2A
•  2B

2B

Q10.  The interior angles of a polygon are in A.P. If the smallest angle be 120° and the common difference be 5, then the number of sides is

•   8
•   10
•   9
•   6

9

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